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<H3>compute rdf command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID rdf Nbin itype1 jtype1 itype2 jtype2 ... 
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
<LI>rdf = style name of this compute command
<LI>Nbin = number of RDF bins
<LI>itypeN = central atom type for Nth RDF histogram (see asterisk form below)
<LI>jtypeN = distribution atom type for Nth RDF histogram (see asterisk form below) 
</UL>
<P><B>Examples:</B>
</P>
<PRE>compute 1 all rdf 100
compute 1 all rdf 100 1 1
compute 1 all rdf 100 * 3
compute 1 fluid rdf 500 1 1 1 2 2 1 2 2
compute 1 fluid rdf 500 1*3 2 5 *10 
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that calculates the radial distribution function
(RDF), also called g(r), and the coordination number for a group of
particles.  Both are calculated in histogram form by binning pairwise
distances into <I>Nbin</I> bins from 0.0 to the maximum force cutoff
defined by the <A HREF = "pair_style.html">pair_style</A> command.  The bins are of
uniform size in radial distance.  Thus a single bin encompasses a thin
shell of distances in 3d and a thin ring of distances in 2d.
</P>
<P>The <I>itypeN</I> and <I>jtypeN</I> arguments are optional.  These arguments
must come in pairs.  If no pairs are listed, then a single histogram
is computed for g(r) between all atom types.  If one or more pairs are
listed, then a separate histogram is generated for each
<I>itype</I>,<I>jtype</I> pair.
</P>
<P>The <I>itypeN</I> and <I>jtypeN</I> settings can be specified in one of two
ways.  An explicit numeric value can be used, as in the 4th example
above.  Or a wild-card asterisk can be used to specify a range of atom
types.  This takes the form "*" or "*n" or "n*" or "m*n".  If N = the
number of atom types, then an asterisk with no numeric values means
all types from 1 to N.  A leading asterisk means all types from 1 to n
(inclusive).  A trailing asterisk means all types from n to N
(inclusive).  A middle asterisk means all types from m to n
(inclusive).
</P>
<P>If both <I>itypeN</I> and <I>jtypeN</I> are single values, as in the 4th example
above, this means that a g(r) is computed where atoms of type <I>itypeN</I>
are the central atom, and atoms of type <I>jtypeN</I> are the distribution
atom.  If either <I>itypeN</I> and <I>jtypeN</I> represent a range of values via
the wild-card asterisk, as in the 5th example above, this means that a
g(r) is computed where atoms of any of the range of types represented
by <I>itypeN</I> are the central atom, and atoms of any of the range of
types represented by <I>jtypeN</I> are the distribution atom.
</P>
<P>Pairwise distances are generated by looping over a pairwise neighbor
list, just as they would be in a <A HREF = "pair_style.html">pair_style</A>
computation.  The distance between two atoms I and J is included in
a specific histogram if the following criteria are met:
</P>
<UL><LI>atoms I,J are both in the specified compute group
<LI>the distance between atoms I,J is less than the maximum force cutoff
<LI>the type of the I atom matches itypeN (one or a range of types)
<LI>the type of the J atom matches jtypeN (one or a range of types) 
</UL>
<P>It is OK if a particular pairwise distance is included in more than
one individual histogram, due to the way the <I>itypeN</I> and <I>jtypeN</I>
arguments are specified.
</P>
<P>The g(r) value for a bin is calculated from the histogram count by
scaling it by the idealized number of how many counts there would be
if atoms of type <I>jtypeN</I> were uniformly distributed.  Thus it
involves the count of <I>itypeN</I> atoms, the count of <I>jtypeN</I> atoms, the
volume of the entire simulation box, and the volume of the bin's thin
shell in 3d (or the area of the bin's thin ring in 2d).
</P>
<P>A coordination number coord(r) is also calculated, which is the sum of
g(r) values for all bins up to and including the current bin.
</P>
<P>The simplest way to output the results of the compute rdf calculation
to a file is to use the <A HREF = "fix_ave_time.html">fix ave/time</A> command, for
example:
</P>
<PRE>compute myRDF all rdf 50
fix 1 all ave/time 100 1 100 c_myRDF file tmp.rdf mode vector 
</PRE>
<P><B>Output info:</B>
</P>
<P>This compute calculates a global array with the number of rows =
<I>Nbins</I>, and the number of columns = 1 + 2*Npairs, where Npairs is the
number of I,J pairings specified.  The first column has the bin
coordinate (center of the bin), Each successive set of 2 columns has
the g(r) and coord(r) values for a specific set of <I>itypeN</I> versus
<I>jtypeN</I> interactions, as described above.  These values can be used
by any command that uses a global values from a compute as input.  See
<A HREF = "Section_howto.html#howto_15">Section_howto 15</A> for an overview of
LAMMPS output options.
</P>
<P>The array values calculated by this compute are all "intensive".
</P>
<P>The first column of array values will be in distance
<A HREF = "units.html">units</A>.  The g(r) columns of array values are normalized
numbers >= 0.0.  The coordination number columns of array values are
also numbers >= 0.0.
</P>
<P><B>Restrictions:</B>
</P>
<P>The RDF is not computed for distances longer than the force cutoff,
since processors (in parallel) don't know about atom coordinates for
atoms further away than that distance.  If you want an RDF for larger
distances, you can use the <A HREF = "rerun.html">rerun</A> command to post-process
a dump file.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_ave_time.html">fix ave/time</A>
</P>
<P><B>Default:</B> none
</P>
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